<p>For example on the SAT if I get four Ds in a row does that mean that it is very likely one of them is wrong?</p>
<p>Not necessarily, there have been instances where four in a row were all right. Assuming absolute randomness, the probablity of getting the same answer four times in a row is 1/125. I wouldn’t worry about the pattern in your answers too much; just go with what you think is the best answer. For example in the June 2012 SAT on one of the Improving Sentences part I must have gotten like 20 B’s. I got really paranoid and I wasted valuable time triple checking every answer. Later I learned from my score report that I got all the Improving Sentences questions right. It just goes to show that you should go with your gut and not worry about the pattern too much.</p>
<p>No.</p>
<p>There is a 1/625 chance you get DDDD, 1/625 chance you get AEBD, 1/625 chance you get CCDA, etc. Since you’re just talking about 4 in a row, we can multiply that by 5 to get 1/125. Thus, given enough practice problems (which isn’t much, actually, if you’re serious in prepping), you’re more than likely to get 4 in a row.</p>
<p>edit: sniped :(</p>
<p>2012 AMC12A. 'Nuff said.</p>
<p>^that</p>
<p>PS imo 10A was easier than 10b, just saying… (this shouldn’t be here, it shoud be on aops…)</p>
<p>For the SAT, I’m pretty sure the College Board does actively avoid 4 of the same answer in a row. [url=<a href=“http://www.lordalford.com/SAT/sat.htm]SAT[/url”>SAT]SAT[/url</a>] mentions it, but doesn’t really offer a citation. I haven’t ever seen 4 in a row for the answers on an official SAT, and I’m nearly certain it doesn’t happen.</p>
<p>I’ve never seen 4 in a row correct on an official CB SAT. If you do, however, get 4 in a row on an actual SAT, you better be completely sure all 4 are correct. I am under the belief that they actively avoid this.</p>
<p>^^^sorry, but I don’t agree. It’s pretty much random, and it does happen every now and then. Now if you get 9 or 10 in a row, then that might be a problem. But 4? That’s pretty normal.</p>
<p>Cheerios, I fully understand the probability of it happening, but I’m pretty sure that the College Board doesn’t completely randomize their answers and have deliberately avoided 4 in a row. Find me an old SAT where it did happen and I’ll believe you.</p>
<p>First of all: there is NO pattern. And semingly “unlikely” things happen all the time if you sample long enouth. [Aside: for REALLY unlikely events, you will have to sample for so long that it dwarfs the age of the universe – making such events effectively “impossible”. That’s what’s going on in the thread about guessing randomly on every question and scoring a 2400. It’s also how to tell a machine generated random list of say heads and tails from a human based list: the human will stay away from runs of 5 or 6 heads in a row, thinking that it isn’t likely.]</p>
<p>In this case, I would have bet a good bit that 4 in a row does in fact happen and that the SAT does not adjust the answers to avoid this. So I picked up the blue book and started checking the answer keys, working from the back. I got to test #7, section 4 and there it is: 20 - 23 are all C. I am not going to check any others, but I bet they are there…</p>
<p>You should judge how confident you are of an answer choice based on the current question and current answer choices. I would not judge my answer choice’s validity based on previous answer choices. To me, the original poster’s logic would lead to loss of focus and misguided doubts.</p>
<p>nope. it’s been known to happen</p>
<p>pckeller, thanks for checking. Of course, the Blue Book’s not the actual test, but I’d say it’s close enough. Good to know.</p>
<p>When my daughter took her SAT she had five in row with the same answer. But they were all correct answers.</p>
<p>If I remember, I believe that this year’s PSAT had 4 in a row on the writing.</p>
<p>Whoops, just checked. It was three in a row; I got the last one wrong.;)</p>
<p>But yeah, as some of the posters above have said it does happen every now and then, it seems.</p>
<p>Four-in-a-row (or more) of the same answer letter has never appeared in the math portions of all the QAS exams since 2005. Not sure about the CR and writing sections, however. Lots of three-in-a-row.</p>
<p>The math answer letters (using the same sample above) are consistent with a uniform p=0.2 distribution for five outcomes.</p>
<p>So here is a related probablilty challenge: If you flip a coin 100 times, what is the probability that you get at least one run of 5 heads in a row? Or if you prefer, what is the probability of getting no such runs?</p>
<p>I believe that this is a hard question, but sometimes probability questions seem hard until you see how to crack them. But unless I am missing something obvious, this is a lot harder than an SAT question. Anybody?</p>
<p>[To be clear: I do NOT have a solution to this challenge…if i come up with something, I’ll post it.]</p>
<p>@pckeller that’s more of an AIME-level question. I think you can do it by trying small cases (5,6 coins) then generalizing to 100. This should work because, for the n+1-th coin flip, you only need to check that the {n-3, …, n+1}th coin flips do not have all heads or all tails.</p>
<p>@pckeller the probability of 5 heads in a row is (1/2)^5=1/(2^5)=1/32</p>
<p>As for the SAT randomness question, remember that the sequence ABCD is just as unlikely as BBBB, which is just as unlikely as ADBA. You only notice when there are 4 in a row because it’s so obvious, but it’s no less likely than the ADBA sequence that you’d never glance twice at.</p>
<p>@ameliab12 you’re flipping 100 coins. Not 5. Question’s a little more complicated…</p>